Ariana Grande's making a full mea culpa -- apologizing for calling out all Americans ... to make a point about obesity.

We're told Ariana's telling people close to her she's embarrassed about the comments she made while in the donut shop ... saying she hates America and Americans.

We're told she was indeed merely reacting to the massive donuts that had just been placed in front of her -- but she realizes her reaction was inappropriate. Our sources say she realizes obesity is a serious issue -- she works with anti-childhood obesity groups -- and she shouldn't have made fun of it.

On the patriotic front -- we're told, "She's a proud American. Especially in light of all the recent progress for equality in our country."

As for the MLB concert ... we're told it's 100% due to the oral surgery she had.

Bottom line ... she put her foot in her mouth, instead of a donut. It happens.

I don't think shell be getting the job of singing The National Anthem anytime soon